Hysteresis and instabilities in a spheroid in precession near the resonance with the tilt-over mode. (23rd December 2020) - Nobili, C.; Meunier, P.; Favier, B.; Le Bars, M.
Abstract: Abstract : This study explores experimentally the flows driven by precession in an oblate spheroid, in the vicinity of the possible resonance with the tilt-over mode. Two main phenomena are reported, combining observations and velocity measurements. First, a hysteretic cycle is quantitatively described between two uniform vorticity solutions, in good agreement with the historical analytical study of Busse ( J. Fluid Mech., vol. 33, 1968, pp. 739–752). We then address the destabilization of each branch at low enough Ekman number. We confirm the possible presence of a so-called conical shear instability, recently depicted in the sphere by Lin et al. ( Phys. Fluids, vol. 27, 2015, 046601) and in the spheroid by Horimoto et al. ( Phys. Rev. Fluids, vol. 5, 2020, 063901). However, available measurements in the accessible parameter range are not sufficient to definitively discard an elliptical or shear origin of the excited instabilities in the spheroid, as first introduced by Kerswell ( Geophys. Astrophys. Fluid Dyn., vol. 72, 1993, pp. 107–144).